Lateral Surface Area of Icosahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
LSA = 9*sqrt(3)/2*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Lateral Surface Area of Icosahedron - (Measured in Square Meter) - Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron.
Space Diagonal of Icosahedron - (Measured in Meter) - The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Icosahedron: 19 Meter --> 19 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LSA = 9*sqrt(3)/2*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2 --> 9*sqrt(3)/2*((2*19)/(sqrt(10+(2*sqrt(5)))))^2
Evaluating ... ...
LSA = 777.692123856426
STEP 3: Convert Result to Output's Unit
777.692123856426 Square Meter --> No Conversion Required
FINAL ANSWER
777.692123856426 777.6921 Square Meter <-- Lateral Surface Area of Icosahedron
(Calculation completed in 00.020 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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Mumbai University (DJSCE), Mumbai
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12 Lateral Surface Area of Icosahedron Calculators

Lateral Surface Area of Icosahedron given Surface to Volume Ratio
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
Lateral Surface Area of Icosahedron given Circumsphere Radius
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Lateral Surface Area of Icosahedron given Insphere Radius
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
Lateral Surface Area of Icosahedron given Space Diagonal
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Lateral Surface Area of Icosahedron given Total Surface Area and Edge Length
​ Go Lateral Surface Area of Icosahedron = Total Surface Area of Icosahedron-sqrt(3)/2*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Midsphere Radius
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
Lateral Surface Area of Icosahedron given Volume
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
Lateral Surface Area of Icosahedron given Face Perimeter
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
Lateral Surface Area of Icosahedron given Perimeter
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Perimeter of Icosahedron/30)^2
Lateral Surface Area of Icosahedron
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Total Surface Area
​ Go Lateral Surface Area of Icosahedron = 9/10*Total Surface Area of Icosahedron
Lateral Surface Area of Icosahedron given Face Area
​ Go Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron

Lateral Surface Area of Icosahedron given Space Diagonal Formula

Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
LSA = 9*sqrt(3)/2*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Lateral Surface Area of Icosahedron given Space Diagonal?

Lateral Surface Area of Icosahedron given Space Diagonal calculator uses Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2 to calculate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron given Space Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the space diagonal of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Icosahedron given Space Diagonal using this online calculator? To use this online calculator for Lateral Surface Area of Icosahedron given Space Diagonal, enter Space Diagonal of Icosahedron (dSpace) and hit the calculate button. Here is how the Lateral Surface Area of Icosahedron given Space Diagonal calculation can be explained with given input values -> 777.6921 = 9*sqrt(3)/2*((2*19)/(sqrt(10+(2*sqrt(5)))))^2.

FAQ

What is Lateral Surface Area of Icosahedron given Space Diagonal?
The Lateral Surface Area of Icosahedron given Space Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the space diagonal of the Icosahedron and is represented as LSA = 9*sqrt(3)/2*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2 or Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
How to calculate Lateral Surface Area of Icosahedron given Space Diagonal?
The Lateral Surface Area of Icosahedron given Space Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the space diagonal of the Icosahedron is calculated using Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. To calculate Lateral Surface Area of Icosahedron given Space Diagonal, you need Space Diagonal of Icosahedron (dSpace). With our tool, you need to enter the respective value for Space Diagonal of Icosahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Lateral Surface Area of Icosahedron?
In this formula, Lateral Surface Area of Icosahedron uses Space Diagonal of Icosahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Lateral Surface Area of Icosahedron = 9/10*Total Surface Area of Icosahedron
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
  • Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
  • Lateral Surface Area of Icosahedron = Total Surface Area of Icosahedron-sqrt(3)/2*Edge Length of Icosahedron^2
  • Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Perimeter of Icosahedron/30)^2
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